Spontaneous symmetry breaking and the flat phase of crystalline membranes

International audienceCrystalline membranes are one of the rare examples of bidimensional systems in which long-range order can stabilize an ordered phase in the thermodynamic limit. By a careful analysis of the Goldstone mode counting, we propose a symmetry-breaking mechanism associated with the generation of the flat phase, and we show how it highlights the crucial role played by the crystalline lattice in the establishment of long-range order in these objects. Comparison with other symmetry-breaking mechanisms in membrane physics is also used to unveil the links between symmetry-breaking patterns and the physical properties of the flat phase